How to Estimate the Supplier Fill Rate When the Supply Order and the Supply Lead-time Are Uncertain?

Document Type : Research Paper

Authors

1 OASIS Laboratory (ENIT-Tunis), National Engineering School of Carthage, University of Tunis El Manar, Tunisia

2 ACS Laboratory, National Engineering School of Tunis, University of Tunis El Manar, Tunisia

Abstract

Modern retail supply chains are more and more exposed to risks and uncertainties. The supply risk such as the uncertainty of the supplier fill rate (SFR) directly affects the performance of a retail supply chain. The purpose of this paper is to investigate the supply uncertainty, where the order size and the supply lead-time are considered as decision variables. We aim at developing a more realistic approach to predict the SFR. The review of the relevant literature was the first step performed. We pointed out that while the scientific research on supply risk is growing, the literature lacks an accurate support tool that can predict the SFR. Then, a case study has been conducted in order to have a comprehensive view of the real context of SFR parameters. Accordingly, we propose a new approach for predicting SFR using bivariate normal distribution. We illustrate the proposed approach using a numerical example of a real case study in Tunisia.

Keywords

Main Subjects


Aastrup, J. and Kotzab, H. (2009). Analyzing out-of-stock in independent grocery stores: an empirical study, International Journal of Retail and Distribution Management, Vol. 37 (9), pp. 765–789.
Bahroun, M. and Harbi, S. (2015). Risk management in the modern retail supply chain: Lessons from a case study and literature review, 6th IESM Conference, October 2015, Seville, Spain.
Ben Hmida, F., Khalfa, S. and Chelbi, A. (2010). Estimation du budget alloué à la garantie bidimensionnelle d’un produit, MOSIM’10, Hammamet, Tunisia, Mai 2010.
Burke, G. J., Carrillo, J. E. and Vakharia, A. J. (2009). Sourcing decisions with stochastic supplier reliability and stochastic demand, Production and Operations Management, Vol. 18(4), pp. 475-484.
Chelbi, A., Soussi, M. A. and Ait-Kadi, D. (2009). Bivariate renewal function computational algorithm, International Conference on Industrial Engineering and Systems Management, Montréal, Canada, mai 2009.
Chen, M., Xia, Y. and Wang, X. (2010). Managing supply uncertainties through Bayesian information update, IEEE Transactions on Automation Science and Engineering, Vol. 7 (1), pp. 24-36.
Chen, J., Lin D. K., and Thomas. D. J. (2003). On the item fill rate for a finite horizon, Operations Research Letters, Vol. 31 (2), pp. 199-123.
Chen, F., Li J. and Zhang. H. (2013). Managing downstream competition via capacity allocation, Production and Operations Management, Vol. 22 (2), pp. 426-446.
Disney, M.S, Gaalman, G.J.C., Hedenstierna, C. T. and Hosoda, T., (2015). Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand, International Journal of Production Economics, Vol. 170 (2015), pp. 501–512.
Du, S., Zhu, Y., Nie, T. Yu, H. (2018). Loss-averse preferences in a two-echelon supply chain with yield risk and demand uncertainty, Oper Res Int J , Vol. 18 , pp. 361-388.
Ehrenthal Joachim, C.F. and Stölzle, W., (2013). An examination of the causes for retail stockouts, International Journal of Physical Distribution and Logistics Management, Vol. 43 (1), pp. 54-69.
Fernie, J., Sparks, L. and McKinnon, A. C. (2010). Retail logistics in the UK: past, present and future", International Journal of Retail and Distribution Management, Vol. 38 (11/12), pp. 894-914.
Gualandris, J., and Kalchschmidt, M., (2015). Supply risk management and competitive advantage: a misfit model, The International Journal of Logistics Management, Vol. 26 (3), pp. 459-478.
Gumus, M., Ray S. and Gurnani. H. (2012). Supply-side story: Risks, guarantees, competition, and information asymmetry, Management Science, Vol. 58 (9), pp. 1694-1714.
Gupta, D. and Cooper, W. L., (2005). Stochastic comparisons in production yield management, Operations research, Vol. 53 (2), pp. 377–384.
Gurnani, H., Ramachandran, K., Ray, S. and Xia, Y. (2013). Ordering behavior under supply risk: An experimental investigation, Manufacturing and Service Operations Management, Vol. 16 (1), pp. 61-75.
Guijarro T. E., Cardós, M. and Babiloni, E., (2012). On the exact calculation of the fill rate under discrete demand patterns, European Journal of Operational Research, Vol. 218 (2), pp. 442–444.
Hamdi, F., Ghorbel, A., Masmoudi, F. Lionel Dupont (2018). Optimization of a supply portfolio in the context of supply chain risk management: literature review, Journal of Intelligent Manufacturing, Vol. 29(4), pp. 763–788
Hosseinia, A. and Zare Mehrjerdi Y. (2016). The Bullwhip Effect on the VMI-Supply Chain Management via System Dynamics Approach: The Supply chain with Two Suppliers and One Retail Channel, Int J Supply Oper Manage (IJSOM), Vol.3(2), pp. 1301-1317.
Hopp, W. J., Iravani, S. M. R. and Liu, F. (2009). Managing white-collar work: An operations-oriented survey, Production and Operations Management, Vol. 18 (1), pp. 1-32.
Hübner, A. H., Kuhn, H., and Sternbeck, M. G. (2013). Demand and supply chain planning in grocery retail: an operations planning framework, International Journal of Retail and Distribution Management, Vol. 41 (7), pp. 512-530.
Käki A, Liesiö J., Salo A. and Talluri S., (2015). Newsvendor decisions under supply uncertainty, International Journal of Production Research, Vol. 53 (5), pp. 1544-1560.
Keren, B. (2009). The single-period inventory problem: Extension to random yield from the perspective of the supply chain, Omega, Vol. 37 (4), pp. 801–810.
Ketkar M., Vaidya O.S. (2018). A Flexible Approach to Mitigation of Supply Risk through Scenario Modelling. In: Sushil, Singh T., Kulkarni A. (eds) Flexibility in Resource Management. Flexible Systems Management. Springer, Singapore.
Larsen, C. and Thorstenson, A., (2014). The order and volume fill rates in inventory control systems, International Journal of Production Economics, Vol. 147, pp. 13–19.
Liang, L. and Atkins D. (2013). Designing service level agreements for inventory management, Production and Operations Management, Vol.  22 (5), pp. 1103–1117.
Nagarajan, M. and Shechter, S. (2013), Prospect theory and the newsvendor problem, Management Science, Vol. 60(4), pp. 1057-1062.
Nasrabadi, M. and Mirzazadeh, A. (2016). The Inventory System Management under Uncertain Conditions and Time Value of Money, Int J Supply Oper Manage (IJSOM), Vol.3 (1). pp. 1192-1214.
Palaro H. P. and Hotta L. K. (2006). Using Conditional Copula to Estimate Value at Risk, Journal of Data Science, Vol. 4, pp. 93-115.
Priyan S. and Uthayakumar R. (2015). Continuous review inventory model with controllable lead time, lost sales rate and order processing cost when the received quantity is uncertain, Journal of Manufacturing Systems, Vol. 34, pp. 23–33.
Ray P. and Jenamani M., (2013). Sourcing under supply disruption with capacity-constrained suppliers, Journal of Advances in Management Research, Vol. 10 (2), pp. 192–205.
Schmitt. A.J. (2008). Using Stochastic Supply Inventory Models to Strategically Mitigate Supply Chain Disruption Risk, Logistics Spectrum, Vol. 42 (4), pp. 22-27.
Schmitt, A.J., Snyder, L.V. and Shen, Z.M. (2010). Inventory Systems with Stochastic Demand and Supply: Properties and Approximations, European Journal of Operational Research, Vol. 206, pp. 313-328.
Sundararajan, R. and Uthayakumar, R. (2015). EOQ model for delayed deteriorating items with shortages and trade credit policy, Int J Supply Oper Manage (IJSOM), Vol.2 (2), pp. 759-783. 
Song, J. and Zipkin P. (2009). Inventories with multiple supply sources and networks of queues with overflow bypasses, Management Science, Vol. 55, pp. 362-372.
Sieke, M. A., Seifert, R. W. and Thonemann. U. W. (2012). Designing service level contracts for supply chain coordination”, Production and Operations Management, Vol. 21 (4), pp. 698-714.
Tang, S.Y. and Kouvelis. P. (2011). Supplier diversification strategies in the presence of yield uncertainty and buyer competition, Manufacturing and Service Operations Management, Vol. 13 (4), pp. 439-451.
Tannous A. and Seongno Yoon (2018). Summarizing Risk, Sustainability and Collaboration in Global Supply Chain Management, Int J Supply Oper Manage (IJSOM), Vol.5 (2), pp. 192-196.
Tempelmeier, H. (2000). Inventory service-levels in the customer supply chain, OR Spectrum, Vol. 22, pp. 361-380.
Teller, C., Kotzab, H., Grant, D., and Holweg, C., (2016). The importance of key supplier relationship management in supply chains, International Journal of Retail and Distribution Management, Vol. 44 (2), pp. 1-16.
Wang, Y., W. Gilland, B. Tomlin. (2010). Mitigating supply risk: dual sourcing or process improvement?, Manufacturing and Service Operations Management, Vol. 12 (3), pp. 489-510.
Wenming C., Srinivas T., and Gyöngyi K., (2018). Investigating the effects of lead-time uncertainties and safety stocks on logistical performance in a border-crossing JIT supply chain”, Computers & Industrial Engineering, Vol. 118, pp. 440-450.
Yang, Z., Aydın, G., Babich, V. and Beil, D. R. (2012). Using a dual-sourcing option in the presence of asymmetric information about supplier reliability: Competition vs. diversification, Manufacturing and Service Operations Management, Vol. 14 (2), pp. 202-217.
Xin Fang, Cheng Zhang, David J. Robb, Joseph D. Blackburn (2013). Decision support for lead time and demand variability reduction, Omega, Vol.41. pp. 390–396.
Yano, C. A. and Lee, H. L. (1995). Lot sizing with random yields: A review, Operations Research, Vol.43 (2), pp. 311-334.
Yue S., Ouarda T. B. M. J., and Bobee B. (2001), A review of bivariate gamma distributions for hydrological application, Journal of Hydrology, Vol.246, pp. 1–18.
Yue S. (2001). A bivariate gamma distribution for use in multivariate flood frequency analysis, Hydrological Processes, Vol. 15, pp. 1033–1045.
Zipkin. P. H. (2000). Foundations of Inventory Management, McGraw-Hill, New York, 2000.
Zsidisin, G.A (2003). Managerial Perceptions of Supply Risk, Journal of Supply Chain Management, Vol.39 (1), pp. 14-25.